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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 17325.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.bh1 | 17325r3 | \([1, -1, 0, -129378942, -566394078659]\) | \(21026497979043461623321/161783881875\) | \(1842819529482421875\) | \([2]\) | \(1474560\) | \(3.0973\) | |
| 17325.bh2 | 17325r2 | \([1, -1, 0, -8091567, -8836015784]\) | \(5143681768032498601/14238434358225\) | \(162184666361656640625\) | \([2, 2]\) | \(737280\) | \(2.7507\) | |
| 17325.bh3 | 17325r4 | \([1, -1, 0, -4902192, -15874966409]\) | \(-1143792273008057401/8897444448004035\) | \(-101347453165545961171875\) | \([2]\) | \(1474560\) | \(3.0973\) | |
| 17325.bh4 | 17325r1 | \([1, -1, 0, -710442, -15571409]\) | \(3481467828171481/2005331497785\) | \(22841979091957265625\) | \([2]\) | \(368640\) | \(2.4042\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 17325.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 17325.bh do not have complex multiplication.Modular form 17325.2.a.bh
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
